WS9

*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Dec 2009 13:22:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur.htm/, Retrieved Fri, 04 Dec 2009 21:23:35 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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14,3 14,2 15,9 15,3 15,5 15,1 15 12,1 15,8 16,9 15,1 13,7 14,8 14,7 16 15,4 15 15,5 15,1 11,7 16,3 16,7 15 14,9 14,6 15,3 17,9 16,4 15,4 17,9 15,9 13,9 17,8 17,9 17,4 16,7 16 16,6 19,1 17,8 17,2 18,6 16,3 15,1 19,2 17,7 19,1 18 17,5 17,8 21,1 17,2 19,4 19,8 17,6 16,2 19,5 19,9 20 17,3

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.200675449151377 beta 0.0641812341628278 gamma 0.793209546372447 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14.8 14.7522708857122 0.0477291142878205 14 14.7 14.6802261467442 0.0197738532557867 15 16 15.9850463960228 0.0149536039771938 16 15.4 15.3822985784913 0.0177014215086970 17 15 15.0053857569075 -0.00538575690746335 18 15.5 15.4640104719269 0.035989528073074 19 15.1 15.0920721822465 0.00792781775353646 20 11.7 12.1474515255814 -0.447451525581389 21 16.3 15.7184899924494 0.581510007550612 22 16.7 16.9362623346833 -0.236262334683264 23 15 15.1112839739173 -0.111283973917345 24 14.9 13.6965351282336 1.20346487176636 25 14.6 15.0868015630430 -0.486801563042963 26 15.3 14.8958255923466 0.40417440765343 27 17.9 16.3128502629540 1.58714973704605 28 16.4 16.0356175554230 0.364382444577032 29 15.4 15.7310352789970 -0.331035278996975 30 17.9 16.2045205816340 1.69547941836603 31 15.9 16.1731589235234 -0.273158923523402 32 13.9 12.7008840273437 1.19911597265633 33 17.8 17.7609591497637 0.0390408502363222 34 17.9 18.4833715355693 -0.583371535569281 35 17.4 16.5674225025693 0.83257749743074 36 16.7 16.1710413704697 0.528958629530273 37 16 16.4232263059147 -0.423226305914714 38 16.6 16.9278212185080 -0.327821218507950 39 19.1 19.2134443381708 -0.113444338170758 40 17.8 17.7337713071873 0.0662286928127145 41 17.2 16.8870152835738 0.312984716426204 42 18.6 18.9695030778725 -0.369503077872515 43 16.3 17.1702752957141 -0.870275295714109 44 15.1 14.3375404840713 0.76245951592867 45 19.2 18.8063545969414 0.393645403058638 46 17.7 19.2234752859687 -1.52347528596867 47 19.1 17.9555079955097 1.14449200449032 48 18 17.3802961189366 0.619703881063401 49 17.5 17.0155417662349 0.484458233765114 50 17.8 17.8099268127378 -0.00992681273780605 51 21.1 20.4787146422039 0.62128535779609 52 17.2 19.1746546782697 -1.97465467826973 53 19.4 18.0291384388512 1.37086156114875 54 19.8 20.0044238261271 -0.204423826127147 55 17.6 17.7805499364049 -0.180549936404915 56 16.2 16.0028708689642 0.19712913103578 57 19.5 20.4239154419124 -0.923915441912413 58 19.9 19.2875439002934 0.612456099706606 59 20 20.2094019111936 -0.209401911193577 60 17.3 18.9532929550498 -1.6532929550498 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 17.9968834836137 16.7529907309122 19.2407762363153 62 18.3621353350573 17.0768431769995 19.6474274931151 63 21.4913322039795 20.1329465365224 22.8497178714365 64 18.2804093998252 16.9166256955926 19.6441931040579 65 19.6826641079580 18.2454356473358 21.1198925685803 66 20.3686555314312 18.8624573517804 21.8748537110819 67 18.1146562375762 16.6127928074393 19.616519667713 68 16.5480518665198 15.0378600490335 18.0582436840061 69 20.2687875226145 18.5645993282179 21.9729757170111 70 20.2704482776843 18.5005152802054 22.0403812751631 71 20.5271288110774 18.6766869185590 22.3775707035958 72 18.3039957835319 -0.150002957186345 36.7579945242501

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/1fre61259958160.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/1fre61259958160.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/26de01259958160.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/26de01259958160.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/3zeb11259958160.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259958211ile6fnt35pvjzur/3zeb11259958160.ps (open in new window)

Parameters (Session):

par1 = 0.2 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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